Faitdream - I got an RFE because my arrest(From not paying a ticket) showed up in my record.

Now, I believe an unpaid ticket will not appear on your record, But, if you have an unpaid ticket, more likely you will have a warrant for your arrest and that might show up on the background check.

If you have unpaid tickets contact the court and make arrangements to remove the warrants (if any) as soon as possible. And besides that. You do not want an arrest for unpaid tickets on your records for life. Believe me.